EXPONENTIAL MOMENTS OF FIRST PASSAGE TIMES AND RELATED QUANTITIES FOR RANDOM WALKS

被引：4

作者：

Iksanov, Alexander ^{[1
]}

Meiners, Matthias ^{[2
]}

机构：

[1] Natl T Shevchenko Univ Kiev, Fac Cybernet, Kiev, Ukraine

[2] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2010年 / 15卷

关键词：

first-passage time; last exit time; number of visits; random walk; renewal theory;

D O I：

10.1214/ECP.v15-1569

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For a zero-delayed random walk on the real line, let tau(x), N(x) and rho(x) denote the first passage time into the interval (x,infinity), the number of visits to the interval (-infinity,x] and the last exit time from (-infinity,x], respectively. In the present paper, we provide ultimate criteria for the finiteness of exponential moments of these quantities. Moreover, whenever these moments are finite, we derive their asymptotic behaviour, as x -> infinity.

引用

页码：365 / 375

页数：11

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